Consider the function f(x) = 2x³ – 3x² + x + 3. Find

(a) The derivative of f(x) from first principles;

(b) The rate of change of f(x) at x = 1;

(c) The points at which the line through (1, 3) with slope m cuts the graph of f(x);

(d) The values of m such that two of the points of intersection found in (c) are coincident;

(e) the equations of the tangents to the graph of f(x) at x = 1 and x = 1/4